In a dozen donuts the probability of getting a chocolate donut is 1/5, meaning 1/5 of the 12 donuts are chocolate donuts.
Step 1.- Calculate how much 1/5 out of 12 is:
[tex]\frac{1}{5}(12)=\frac{12}{5}=2.4[/tex]In each dozen we would get 2.4 chocolate donuts
Step 2.- Calculate how many dozen are needed to get 271 chocolate donuts.
We divide 271 by 2.4 to get the answer:
[tex]\frac{271}{2.4}=112.92[/tex]Step 3: We round the answer to the nearest integer value, and we need 113 dozens of donuts to ensure that all 271 people get a chocolate donut.
Answer: 113
The volume of gas kept at a constant pressure varies inversely with the temperature T. If the temperature is 50 degrees, the volume is 20 quick feet. What will the volume be when the temperature is 100 degrees. V= , Temperature=. . Solution
Given that the volume of gas kept at constant pressure varies inversely with the temperature T and when the temperature is 50 degrees, the volume is 20 cubic feet.
We have to find the volume of gas when the temperature is 100 degrees.
Since it is given that volume varies inversely with the temperature. It means
[tex]T_1V_1=T_2V_2[/tex]Substitute T1 = 50, V1 = 20, T2 = 100.
[tex]\begin{gathered} 50\times20=100\times V_2 \\ 1000=100\times V_2 \\ \frac{1000}{100}=V_2 \\ 10=V_2 \end{gathered}[/tex]Thus, the volume of gas when the temperature is 100 degrees is 10 cubic feet.
I need help on this, I need it answered in steps
Let's solve the given logarithmic expression:
[tex]\text{ log}_4(64)\text{ = m}[/tex]We get,
[tex]\text{ log}_4(64)\text{ = m}[/tex][tex]\mathrm{Factor\: the\: number\colon\: }\: 64=4^3[/tex][tex]=\log _4\mleft(4^3\mright)[/tex][tex]\mathrm{Apply\: log\: rule}\colon\quad \log _a\mleft(a^x\mright)=x[/tex][tex]\log _4\mleft(4^3\mright)\text{ = 3 = m}[/tex]Therefore, m = 3.
A 3 dimensional shape is created when the shape isrotated around the y-axisFind the volumen of shape
By rotating the shape of the graph, we get the following cylinder:
So we have a cylinder with:
• radius r = 4,
,• height h = 6.
The volume of the cylinder using π = 3.14 is given by:
[tex]V=\pi *r^2*h=3.14*4^2*6=301.44.[/tex]AnswerThe solid obtained is a cylinder of volume 301.44.
aThecity of Huntsville, TX has approximately 25,000 registered voters. There are two candidates forcity council in an upcoming election: Brown and Solano. The day before the election, a telephone pollof 550 randomly selected registered voters was conducted. 243 said they'd vote for Brown, 253 saidthey'd vote for Solano, and 54 were undecided.give the simple statistic for the proportion of voters surveyed
The surveyors are really interested in all registered boters in Huntsville, therefore the first answer is F.
Since they are only doing a sample of people with phones the real population is all registered voters with telephones, therefore the second answer is C.
The sample for this survey is the 550 voter surveyed.
To find the proportion of people who said they vote for brown we divide the number of this people by the total of people surveyed:
[tex]\frac{243}{550}=0.4418[/tex]Therefore the proportion was 0.4418
f(×) = 3× + 7 f(1) =
f(1) = 10
Explanation:Given f(x) = 3x + 7
To find f(1), replace x by 1 in the equation above
f(1) = 3(1) + 7
= 3 + 7
= 10
What is the solution to the linear equation 2/5+p=4/5+3/5p
Ok ,we need to find p in the following equation: 2/5+p=4/5+3/5p, lets
4x + 8 = 28Describe a real-world situation the equation could represent.
In a club, the entrance ticket is $8. And every time you order a soda you have to pay $4 per can. Since you only have $28 in your pocket, how many sodas can you afford?
The equation 4x +8=28 could be used to describe a scenario like this below:
In a club, the entrance ticket is $8. And every time you order a soda you have to pay $4 per can. Since you only have $28 in your pocket, how many sodas can you afford?
Notice the fixed amount (8) and the variable (4x) and the total of money you have (28). So the sum above describes the amount of money for that club.
With that equation you can find that:
4x +8=28
4x+8 -8 =28-8
4x=20
x=5
5 cans of soda.
1. P(video games and kid is 10 to 12 years old)2. P(basketball/kid is 13 to 15 years old)3. P(kid is 13 to 15 years old/basketball)4. P(darts/kid is 10 to 15 years old)5. P(basketball and darts)6. P(basketball and kid is 13 to 18 years old)Answer the following problems about two way frequency tables fill in the missing cells on table and make sure to reduce your fraction.
Horizontal addition
Row 1 a + 12 + b +6 =37
[tex]\begin{gathered} a+12+b+6=37 \\ a+b+18=37 \\ a+b=37-18 \\ a+b=19 \end{gathered}[/tex]Row 2
[tex]\begin{gathered} 8+c+16+11=d \\ c+35=d \end{gathered}[/tex]Row 3
[tex]\begin{gathered} 17+5+e+18=f \\ 40+e=f \end{gathered}[/tex]Row 4
[tex]\begin{gathered} g+34+45+h=143 \\ g+h+79=143 \\ g+h=143-79 \\ g+h=64 \end{gathered}[/tex]Now Let us add the columns
Column 1
[tex]a+8+17=g[/tex]Column 2
[tex]\begin{gathered} 12+c+5=34 \\ c+17=34 \\ c=34-17 \\ c=17 \end{gathered}[/tex]Column 4
[tex]\begin{gathered} 6+11+18=h \\ h=35 \end{gathered}[/tex]Column 2
[tex]\begin{gathered} b+16+e=45 \\ b+e=45-16 \\ b+e=29 \end{gathered}[/tex]Hence, Video games under 10-12 is c=17, gotten from column 2
Vertical total under 16-18 is h=35 gotten from column 4
Hence, the horizontal total of the video game is 52
Since h is gotten, we can solve for 7 to 9 vertical total
[tex]\begin{gathered} g+h=64 \\ g=64-h \\ g=64-35 \\ g=29 \end{gathered}[/tex]Hence, the 7 to 9 vertical total is 29
[tex]\begin{gathered} a+25=g \\ a=g-25 \\ a=29-25 \\ a=4 \end{gathered}[/tex]Hence, Darts under 7 to 9 is 4
Darts under 13 to 15 is b
[tex]\begin{gathered} a+b=19 \\ b=19-a \\ b=19-4 \\ b=15 \end{gathered}[/tex]Hence, Darts under 13 to 15 is 15
Basket ball under 13 to 15 is e
[tex]\begin{gathered} b+e=29 \\ e=29-b \\ e=29-15 \\ e=14 \end{gathered}[/tex]Hence, Darts under 13 to 15 is 14
Video Games Horizontal total is d,
[tex]\begin{gathered} c+35=d \\ 17+35=d \\ d=52 \end{gathered}[/tex]Hence, the Horizontal total of the Video game is 52
Basketball horizontal total is f
40+e=f
[tex]\begin{gathered} 40+e=f \\ 40+14=f \\ 54=f \end{gathered}[/tex]Hence, the horizontal total of the Video game is 54.
Hence, the above table fill the empty space
im on a bit of a time crunch so please hurry :)
Answer
39 child tickets were sold that day
Step-by-step explanation
Variables
• x: child tickets sold
,• y: adult tickets sold
Given that four times as many adult tickets as child tickets were sold, then:
[tex]y=4x[/tex]If 1 child ticket cost $5.70, then x child tickets will cost 5.7x dollars.
If 1 adult ticket cost $9.20, then y adult tickets will cost 9.2y dollars.
Given that the theater sold tickets for $1657.50, then:
[tex]5.7x+9.2y=1657.5[/tex]Substituting the first equation into the second one and solving for x:
[tex]\begin{gathered} 5.7x+9.2(4x)=1,657.5 \\ 5.7x+36.8x=1,657.5 \\ 42.5x=1,657.5 \\ \frac{42.5x}{42.5}=\frac{1,657.5}{42.5} \\ x=39 \end{gathered}[/tex]Write the slope-intercept (y = mx + b) form of an equation for a line with y-intercept-5 and slope 2.
The slope-intercept form of the line is
[tex]y=mx+b[/tex]where m is the slope and b is the y-intercept
so we only need to substitute the values into the equation
m=2
b= -5
the equation is
[tex]y=2x-5[/tex]What rule describes the translation that was applied to triangle JKM to create triangle J’K’M’, Initial directions with the pic below.
Given a point (x, y), let's evaluate the transformations:
- Translation 6 units to the right.
Means moving the point 6 units in the horizontal direction; to the right.
The new point will be (x + 6, y).
- Translation 2 units down.
Means moving the point 2 units down; in the vertical direction.
The new point will be (x + 6, y - 2).
Answer: (x + 6, y - 2).
Which triangle congruence postulate or theorem proves that these triangles are congruent?
The AAS triangle congruence postulate proves that these triangles are congruent .
In the question,
two triangles are given that are triangle ABC and triangle PQR .
Consider the triangle ABC and triangle PQR .
we can see that
(i) angle C = angle R .....given in the figure
(iii) angle B = angle Q .... given in the figure
(ii) side BC = side QR ....given in the figure
From the above three statements we conclude that
ΔABC ≅ ΔPQR
both the triangles KLM and PQR are congruent by AAS Congruence Postulate .
Therefore , The AAS triangle congruence postulate proves that these triangles are congruent .
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Find the equation for the line that passes through the point (3.-5), and that is perpendicular to the line with the equation x = -2
• Line x = -2 is a vertical line that passes through point x = -2
Given the point ( 3;-5)
• We know that perpendicular lines have opposite reciprocal slopes , so the slope of the line will be
,• m = 1/2
• so , the standard formula for a line : y = mx +c
at point ( 3-5) , we will have :
-5 = 1/2(3) + c
Therefore c = -5 -3/2
= -13/2
• Our y- intercept will be -13/2
• Finally , our equation of the line will be :
y = 1/2x -13/2
what is the value of x to the nearest tenth on problem 5
Answer:
Explanation:
In problem 5, we can see that there is a right triangle with legs x and 16 and a hypotenuse equal to (x + 8).
So, by Pythagorean theorem, we can write the following equation
[tex](x+8)^2=x^2+16^2[/tex]Now, we can expand the left side
[tex]\begin{gathered} x^2+2(8)(x)+8^2=x^2+16^2 \\ x^2+16x+64=x^2+256 \end{gathered}[/tex]Then, subtract x² from both sides
[tex]\begin{gathered} x^2+16x+64-x^2=x^2+256-x^2 \\ 16x+64=256 \end{gathered}[/tex]Subtract 64 from both sides
[tex]\begin{gathered} 16x+64-64=256-64 \\ 16x=192 \end{gathered}[/tex]Finally, divide by 16
[tex]\begin{gathered} \frac{16x}{16}=\frac{192}{16} \\ \\ x=12 \end{gathered}[/tex]Therefore, the value of x is 12
someone please help I don't get it!!
Answer:
which one
Step-by-step explanation:
don't forget to follow rate like
Given: the function f defined by f(x) = 3x^2. Which statement is true?
The given function is
[tex]f(x)=3x^2[/tex]If we evaluate the function when x = 0, we get
[tex]f(0)=3(0)^2=3\cdot0=0[/tex]Hence, the first option is correct.If the rate of inflation is 2.5% per year, the future price P(T) in dollars of a certain item can be modeled by the following exponential function, where T is the number of years from today
Solution:
The future price p(t), in dollars, can be modelled by the exponential function;
[tex]p(t)=800(1.025)^t[/tex](a) The current price is;
[tex]\begin{gathered} t=0; \\ \\ p(0)=800(1.025)^0 \\ \\ p(0)=800(1) \\ \\ p(0)=800 \end{gathered}[/tex]ANSWER: $800
(b) The price 8 years from today;
[tex]\begin{gathered} t=8 \\ \\ p(8)=800(1.025)^8 \\ \\ p(8)=800(1.2184) \\ \\ p(8)=974.72 \\ \\ p(8)\approx975 \end{gathered}[/tex]ANSWER: $975
i need to know which one is the answer , i’m having a hard time figuring it out
Answer:
Explanation:
Here, we want to know the table that represents a function
For a relationship to represent a function, no two y values can have a single x value but two x values can have a single y value.
What this means is that two independent variable values can take a single dependent variable value but no two dependent variable values can take a single independent variable value
Now, looking at the table given:
Can you help me with number 11? Thank you I am having trouble with it.
N 11
Remember that
The law of sines
[tex]\frac{a}{\sin A}=\frac{b}{\sin B}=\frac{c}{\sin C}[/tex]In this problem
[tex]\frac{14.9}{\sin X^o}=\frac{25.5}{\sin 71^o}[/tex]Solve for x
sinX=(14.9*sin71)/25.5
Rewrite the area formula with the info given from the problem then find the value of x , then how many feet of fencing should me Korber buy ?
Since the triangle is a right isosceles triangle and each leg measures x, its area is given by:
[tex]A=\frac{1}{2}x^2[/tex]Now, let's use the given area and solve it for x:
[tex]\begin{gathered} 4232=\frac{1}{2}x^2\\ \\ x^2=8464\\ \\ x=92\text{ ft} \end{gathered}[/tex]Since the "path" already has fence, the amount of fence needed is 2x:
[tex]2x=2\cdot92=184\text{ ft}[/tex]Write the point-slope form of the equation of the line through the points (-1, -1) and (2, 4)
The point-slope form of (-1, -1) and (2, 4) is y = 5/3(x+1) - 1.
The point-slope form is simply writing an equation of a line so that the slope or steepness and x-intercept i.e. where the line crosses the vertical x-axis are immediately apparent.
The slope-intercept equation is y - y1 = m(x - x1), where x and y are two variables, and m is the slope.
Slope m = (y2-y1) / (x2-x1)
Let,
(x1, y1) = (-1, -1)
(x2, y2) = (2, 4)
Slope (m) = ((4) - (-1)) / ((2) - (-1))
= 5/3
y - y1 = m(x - x1) => (y - (-1)) = 5/3(x - (-1))
=> y+1 = 5/3(x + 1)
=>y = 5/3(x+1)-1
Therefore, the point-slope form of (-1, -1) and (2, 4) is y = 5/3(x+1)-1.
To know more about point-slope form:
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Two jets leave harrisburg at the same time, one flying east at a speed of 20 km/h greater than the other, which is flying west. After 4 h, the planes are 6000 km apart. Find their speeds. A tourist bus leaves Richmond at 1:90 PM for New York City. Exactly 24 minutes later, a truck sets out in the same direction. The tourist bus moved at a steady 60 km/h. The truck travels at 80 km/h. How long does it take the truck to overtake the tour bus?
We know that two jets leave Harrisburg at the same, time, one flying east, and another flying west.
We will denote the speed of the second jet by x (in km/h). Thus, the speed of the first jet is x+20. Remembering that:
[tex]v=\frac{d}{t}[/tex]where v is speed, d is distance and t is time, we know that for the first jet:
[tex]x+20=\frac{d_1}{4}\Rightarrow4x+80=d_1[/tex]Where d₁ represents the distance of the first jet from the starting point. For the second jet:
[tex]x=\frac{d_2}{4}\Rightarrow4x=d_2[/tex]Where d₂ represents the distance of the second jet from the starting point.
We also know that:
[tex]d_1+d_2=6000[/tex]As:
Thus, we have that:
[tex]\begin{gathered} (4x+80)+(4x)=6000 \\ \text{And solving for x, we get:} \\ 8x+80=6000 \\ 8x=5920 \\ x=\frac{5920}{8}=740 \end{gathered}[/tex]This means that the second jet has a speed of 740km/h, and the first jet has a speed of 760km/h (20km/h greater than the second one).
The USDA collects and distributes a wide variety of data about agriculture in the United States. One statistic reported each year is the number of milk cows (in thousands) in each state. A random sample of 10 states is selected, with the number of milk cows reported in both 2011 and 2015.
State 2011 2015 Difference
North Dakota 19 16 -3
California 1769 1778 9
Nevada 29 29 0
Ohio 268 267 -1
New Hampshire 14 14 0
Colorado 128 146 18
Minnesota 468 460 -8
Oklahoma 53 39 -14
Utah 93 96 3
Washington 260 277 17
mean 310.1 312.2 2.1
sd 532.857 535.367 10.159
An agricultural researcher wants to conduct a paired difference test to determine if the mean number of milk cows (in thousands) in the US changed between 2011 and 2015.
Round all calculated values to 4 decimal places as appropriate.
1. Which hypotheses should be used to conduct the test?
A. H0:μdiff=0 vs. Ha:μdiff≠0
B. H0:μdiff<2.1 vs. Ha:μdiff>2.1
C. H0:μdiff=0 vs. Ha:μdiff<0
D. H0:μdiff=0 vs. Ha:μdiff>0
2. Assume the conditions for the hypothesis test are met and find the test statistic and the p-value.
test statistic =
p-value =
3. Based on the p value we have
?
evidence that the null model is not a good fit for our observed data.
4. Construct a 99% confidence interval for the mean difference in the number of milk cows (in thousands) between 2011 and 2015.
1. The hypothesis tested are given as follows: A. H0:μdiff=0 vs. Ha:μdiff≠0.
2.
The test statistic is of: t = 0.65.The p-value is of: 0.26603. Based on the p-value, we do not have enough evidence that the null model is not a good fit for our observed data.
4. The 99% confidence interval for the mean difference in the number of milk cows (in thousands) between 2011 and 2015 is of (-8.34, 12.54).
What are hypothesis tested?At the null hypothesis, it is tested if there has not been change, that is, if the mean is of zero, hence:
H0:μdiff=0
At the alternative hypothesis, it is tested if there has been change, hence:
Ha: μdiff≠0
Considering a two-tailed test, as we are testing if the mean is different of a value, with 10 - 1 = 9 df, and a significance level of 1 - 0.99 = 0.01, the critical value is of:
|t| = 3.25.
What is the test statistic?The test statistic for the t-distribution is given by the equation presented as follows:
[tex]t = \frac{\overline{x} - \mu}{\frac{s}{\sqrt{n}}}[/tex]
The parameters are:
[tex]\overline{x}[/tex] is the sample mean.[tex]\mu[/tex] is the value tested at the null hypothesis.s is the standard deviation of the sample.n is the sample size.The parameters in this problem are given as follows:
[tex]\overline{x} = 2.1, s = 10.159, n = 10, \mu = 0[/tex]
Hence the test statistic is of:
[tex]t = \frac{\overline{x} - \mu}{\frac{s}{\sqrt{n}}}[/tex]
[tex]t = \frac{2.1 - 0}{\frac{10.159}{\sqrt{10}}}[/tex]
t = 0.65.
What are the p-value and the conclusion?Considering a two-tailed test, with t = 0.65 and 10 - 1 = 9 df, the p-value is of:
0.2660.
What is the confidence interval?The confidence interval is given as the estimate plus/minus the multiplication of the critical value and the standard error.
Hence the lower bound of the interval is of:
2.1 - 3.25x10.159/sqrt(10) = -8.34.
The upper bound of the interval is of:
2.1 + 3.25x10.159/sqrt(10) = 12.54.
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In the image below, line ris perpendicular to both lines p and q. Lines p and p and r. are parallel to one another. Transversal s goes through lines p 28° s What is the value of x? A 62 OB. 72 O C 152 OD. 162 Sign out INTL 2
In this problem we have that
m by supplementary angles
so
mmtherefore
the answer is
x=52 degreesPart 2
the transformations that produce triangle ABC are
1) A dilation from the with scale factor of 2
2) A reflection across the x-axis
3) A translation of
Mia made a pencil box in the shape of a right rectangular prism what's the surface area of the box 20cm,6cm,7cm
1) Let's visualize it to better understand:
A right rectangular prism is made from
2 faces 6 x 7
4 faces 20 x 6
Since we have rectangles, we can write calculating the area of each rectangle.
S base = 2 (6x 7) ⇒ S base = 84 cm²
S faces = 2 (20 x 6) ⇒ S faces = 240 cm²
S faces = 2 (20 x 7) ⇒ S faces = 280 cm²
2) Then the total surface area
84+240+280=604 cm²
trey is draining an aquarium. the graph shows the amount of water (in liters) in the aquarium versus time (in minutes)
Given the graph represents the amount of water in the aquarium versus time.
A) As shown in the graph :
as the time increases the amount of water in the aquarium decreases
The rate of water decreasing =
[tex]\frac{480}{8}=60[/tex]so, the rate = 60 litres per minute
Marcus is playing dodge ball with hisfriends. He catches 2 out of every 5 ballsthrown in his direction. If he catches14 balls, how many balls were thrownat him?balls
Step 1
Given;
[tex]\begin{gathered} \text{Marcus is playing dodge ball with his friends.} \\ He\text{ catches 2 out of every 5 balls thrown in his direction.} \end{gathered}[/tex]Required; To find out how many balls are thrown at him if he catches 14 balls.
Step 2
There are two approaches to determine the number of balls thrown at Marcus
Approach 1
[tex]\begin{gathered} \text{Marcus catches 2 balls for every 5 balls thrown in his direction.} \\ we\text{ can draw up a table and add up 2 balls caught and 5 balls } \\ \text{thrown respectively until we arrive at 14 balls caught.} \end{gathered}[/tex]Draw the table;
we will now sum the total number of balls caught by Marcus and the total number of balls thrown at him to find out he had 35 balls thrown at him when 14 balls were caught by him.
Answer=35 balls
Approach 2
[tex]\begin{gathered} We\text{ will use the ratio} \\ \frac{2\text{ balls caught}}{14\text{ balls caught}}=\frac{5\text{ balls thrown }}{x\text{ balls thrown}} \\ \text{cross multiply} \\ 2x=5(14) \\ \text{simplify} \\ 2x=70 \\ \text{divide both sides by 2} \\ \frac{2x}{2}=\frac{70}{2} \\ x=35\text{ balls thrown} \end{gathered}[/tex]Hence, 35 balls were thrown at Marcus
the density of aluminum is 2700 kg/m3. what is the mass of a solid cube of aluminum with side lengths of 0.5 meters?
SOLUTION
Density is calculated as
[tex]\begin{gathered} Density=\frac{mass}{volume} \\ \end{gathered}[/tex]The side lengths of the aluminium cube has been given as 0.5 m
The volume becomes
[tex]\begin{gathered} volume=length\times length\times length \\ V=L\times L\times L \\ V=0.5\times0.5\times0.5=0.125m^3 \end{gathered}[/tex]so the volume is 0.125 cubic-meters.
The mass becomes
[tex]\begin{gathered} Density=\frac{mass}{volume} \\ mass=density\times volume \\ mass=2700\times0.125 \\ =337.5 \end{gathered}[/tex]Hence the answer is 337.5 kg
-2( 4 - 6h ) +9-8 - 12h + 9-12h + 1Explain the error in the work.
The error is in the distribution property application, in the way the signs are multiplied.
We will look at it in detail:
[tex]\begin{gathered} -2(4-6h)+9 \\ \lbrack(-2)(4)+(-2)(-6h)\rbrack+9 \\ (-8+12h)+9 \\ 12h+1 \end{gathered}[/tex]When (-2) is multiplied by (-12h) it should end with a positive sign, as (-a)*(-b)=a*b
Question #10: Given triangle A is the pre image and B is the image, state the scale factor of the dilation from A to B. * 4 B 10 18 А 7.2 15
To find the acale factor we need to solve the following equation:
[tex]\begin{gathered} 18k=7.2 \\ k=\frac{7.2}{18} \\ k=0.4 \end{gathered}[/tex]This comes from the fact that the biggest sides of both triangles have to be realted.
Therefore the dilation factor is 0.4.